P336. 7. The capacities ( in ampere-hours) were measured for a sample of 120 batteries. The average was 178 and the standard deviation was 14. (a) Find a 95% confidence interval for the mean capacity of batteries produced by this method. (b) Find a 99% confidence interval for the mean capacity of batteries produced by this method. (c) An engineer claims that the mean capacity is between 176 and 180 ampere-hours. With what level of confidence can this statement be made? (d) Approximately how many batteries must be sampled so that a 95% confidence interval will specify the mean to within ±2 ampere-hours? (e) Approximately how many batteries must be sampled so that a 99% confidence interval will specify the mean to within ±2 ampere-hours?

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

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step-by-step explanation: